Estimating Square Roots

Name: _______________________________
Date: _______________________________

Remember: Perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...

To estimate a square root, find the two perfect squares it falls between.

Example: √20 is between √16 and √25, so √20 is between 4 and 5.

Part A: Between Which Two Whole Numbers?

Write the two consecutive whole numbers that each square root falls between.

1. √8 _______ < √8 < _______
2. √30 _______ < √30 < _______
3. √50 _______ < √50 < _______
4. √75 _______ < √75 < _______
5. √110 _______ < √110 < _______
6. √95 _______ < √95 < _______

Part B: Closer To Which Whole Number?

Circle whether each square root is closer to the smaller or larger whole number.

7. √12 Closer to: 3 or 4
8. √40 Closer to: 6 or 7
9. √60 Closer to: 7 or 8
10. √90 Closer to: 9 or 10

Part C: Order the Square Roots

Arrange these numbers from smallest to largest.

11. √15, 4, √10, 5
_______ < _______ < _______ < _______
12. √80, 9, √70, 10
_______ < _______ < _______ < _______

Part D: Challenge

13. A square has an area of 45 cm². Estimate the length of one side to the nearest whole number.

Side length ≈ _______ cm

14. Which is larger: √50 or 7? Explain your reasoning.

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